DIFFERENTIATION

posted by Anonymous

An open topped taking tin with a volume of 864 cm is to be constructed with a square base and vertical sides. Find the least amount of tin plate required.

  1. Steve

    if the base has side x and the tin has height y, then

    x^2 y = 864
    y = 864/x^2

    The surface area a is

    a = x^2 + 4xy = x^2 + 4x(864/x^2)
    = x^2 + 3456/x

    da/dx = 2x - 3456/x^2
    = (2x^3-3456)/x^2
    da/dx=0 when x=12.

    Now find the area.

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